A horizontal spring-mass system has low friction, spring stiffness 205 N/m, and mass 0.6 kg. The system is released with an initial compression of the spring of 13 cm and an initial speed of the mass of 3 m/s.
(a) What is the maximum stretch during the motion? m
(b) What is the maximum speed during the motion? m/s
(c) Now suppose that there is energy dissipation of 0.02 J per cycle of the spring-mass system. What is the average power input in watts required to maintain a steady oscillation?

a) x_max = 0.20794 m

b)  v_max = 3.8436 m/s

c) P = 0.05883 W

Explanation:

Given:

- The stiffness k = 205 N / m

- The mass m = 0.6 kg

- initial compression of the spring xi = 13 cm

- initial speed of the mass vi = 3 m/s

Find:

(a) What is the maximum stretch during the motion? m

(b) What is the maximum speed during the motion? m/s

(c) Now suppose that there is energy dissipation of 0.02 J per cycle of the spring-mass system. What is the average power input in watts required to maintain a steady oscillation?

Solution:

- Conservation of energy principle can be applied that the total energy U of the system remains constant. So the Total energy is:

                          U = K.E + P.E

                          U = 0.5*m*v^2 + 0.5*k*x^2

- We will take initial point with given values and maximum compression x_max when v = 0.

                          0.5*m*vi^2 + 0.5*k*xi^2 = 0.5*k*x_max^2

                          (m/k)*vi^2 + xi^2 = x_max^2

                          x_max = sqrt ( (m/k)*vi^2 + xi^2 ) = sqrt ( (.6/205)*3^2 + .13^2  

                          x_max = 0.20794 m

- The angular speed w of the harmonic oscillation is given by:

                          w = sqrt ( k / m )

                          w = sqrt ( 205 / 0.6 )

                          w = 18.48422 rad/s

- The maximum velocity v_max is given by:

                          v_max = - w*x_max

                          v_max = - (18.48422)*(0.20794)

                          v_max = 3.8436 m/s

- The amount of power required to stabilize each oscillation is given by:

                         P = E_cycle / T

Where, E = Energy per cycle  = 0.02 J

             T = Time period of oscillation

                         T = 2π/w

                         P = E_cycle*w / 2π

                         P = (0.02*18.48422) / 2π

                         P = 0.05883 W

i just did an experiment like this in my science class. also the answer is yes, it will get separated because they are two opposites meaning if they are opposite they can not attract.

hope this .!